Question: Solve for $x$ and $y$ using elimination. ${-3x-3y = -39}$ ${x+4y = 43}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $3$ ${-3x-3y = -39}$ $3x+12y = 129$ Add the top and bottom equations together. $9y = 90$ $\dfrac{9y}{{9}} = \dfrac{90}{{9}}$ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into $\thinspace {-3x-3y = -39}\thinspace$ to find $x$ ${-3x - 3}{(10)}{= -39}$ $-3x-30 = -39$ $-3x-30{+30} = -39{+30}$ $-3x = -9$ $\dfrac{-3x}{{-3}} = \dfrac{-9}{{-3}}$ ${x = 3}$ You can also plug ${y = 10}$ into $\thinspace {x+4y = 43}\thinspace$ and get the same answer for $x$ : ${x + 4}{(10)}{= 43}$ ${x = 3}$